Résolution d'inéquation

variations autour de k

X

Y

\leq

\geq

\lt

\gt

Afficher la correction

Masquer la correction

A101 = NaN
A52 = If(A101 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A101 ≟ 1, Random[0, 1], Random[-1, 0]])
A53 = NaN
H = Random(4, 7)
n = Random(3, 6)
A4 = If(A53 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A53 ≟ 1, Random[0, 1], Random[-1, 0]])
A54 = NaN
A5 = If(A54 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A54 ≟ 1, Random[0, 1], Random[-1, 0]])
k: Random[-2, 7] + n - n
C52 = If(A52 ≟ 0, k, If[A52 ≟ 1, k + Random[3, H], k - Random[3, H]])
C4 = If(A4 ≟ 0, k, If[A4 ≟ 1, k + Random[3, H], k - Random[3, H]])
C5 = If(A5 ≟ 0, k, If[A5 ≟ 1, k + Random[3, H], k - Random[3, H]])
A2: Random[-1, 1] + n - n
C2 = If(A2 ≟ 0, k, If[A2 ≟ 1, k + Random[3, H], k - Random[3, H]])
A3 = If(A2 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A2 ≟ 1, Random[0, 1], Random[-1, 0]])
C3 = If(A3 ≟ 0, k, If[A3 ≟ 1, k + Random[3, H], k - Random[3, H]])
b: (n * 3) + Random[0, 4]
a: Random[-5, 1] + n - n
h = Max((b - a) / n, 3)
B2: a
A: (B2, C2)
B3: B2 + floor(Random[(3 * h / 4), (5 * h / 4)])
B: (B3, C3)
B4: B3 + floor(Random[(3 * h / 4), (5 * h / 4)])
C: (B4, C4)
B5: B4 + floor(Random[(3 * h / 4), (5 * h / 4)])
E: (B5, C5)
B6: B5 + floor(Random[(3 * h / 4), (5 * h / 4)])
B7: B6 + floor(Random[(3 * h / 4), (5 * h / 4)])
B8: B7 + floor(Random[(3 * h / 4), (5 * h / 4)])
B9: B8 + floor(Random[(3 * h / 4), (5 * h / 4)])
B10: B9 + floor(Random[(3 * h / 4), (5 * h / 4)])
B11: B10 + floor(Random[(3 * h / 4), (5 * h / 4)])
B12: B11 + floor(Random[(3 * h / 4), (5 * h / 4)])
B13: B12 + floor(Random[(3 * h / 4), (5 * h / 4)])
B14: B13 + floor(Random[(3 * h / 4), (5 * h / 4)])
B15: B14 + floor(Random[(3 * h / 4), (5 * h / 4)])
B16: B15 + floor(Random[(3 * h / 4), (5 * h / 4)])
B17: B16 + floor(Random[(3 * h / 4), (5 * h / 4)])
B18: B17 + floor(Random[(3 * h / 4), (5 * h / 4)])
B19: B18 + floor(Random[(3 * h / 4), (5 * h / 4)])
B20: B19 + floor(Random[(3 * h / 4), (5 * h / 4)])
B21: B20 + floor(Random[(3 * h / 4), (5 * h / 4)])
B22: B21 + floor(Random[(3 * h / 4), (5 * h / 4)])
B23: B22 + floor(Random[(3 * h / 4), (5 * h / 4)])
B24: B23 + floor(Random[(3 * h / 4), (5 * h / 4)])
B25: B24 + floor(Random[(3 * h / 4), (5 * h / 4)])
B26: B25 + floor(Random[(3 * h / 4), (5 * h / 4)])
B27: B26 + floor(Random[(3 * h / 4), (5 * h / 4)])
B28: B27 + floor(Random[(3 * h / 4), (5 * h / 4)])
B29: B28 + floor(Random[(3 * h / 4), (5 * h / 4)])
B30: B29 + floor(Random[(3 * h / 4), (5 * h / 4)])
B31: B30 + floor(Random[(3 * h / 4), (5 * h / 4)])
B32: B31 + floor(Random[(3 * h / 4), (5 * h / 4)])
B33: B32 + floor(Random[(3 * h / 4), (5 * h / 4)])
B34: B33 + floor(Random[(3 * h / 4), (5 * h / 4)])
B35: B34 + floor(Random[(3 * h / 4), (5 * h / 4)])
B36: B35 + floor(Random[(3 * h / 4), (5 * h / 4)])
B37: B36 + floor(Random[(3 * h / 4), (5 * h / 4)])
B38: B37 + floor(Random[(3 * h / 4), (5 * h / 4)])
B39: B38 + floor(Random[(3 * h / 4), (5 * h / 4)])
B40: B39 + floor(Random[(3 * h / 4), (5 * h / 4)])
B41: B40 + floor(Random[(3 * h / 4), (5 * h / 4)])
B42: B41 + floor(Random[(3 * h / 4), (5 * h / 4)])
B43: B42 + floor(Random[(3 * h / 4), (5 * h / 4)])
B44: B43 + floor(Random[(3 * h / 4), (5 * h / 4)])
B45: B44 + floor(Random[(3 * h / 4), (5 * h / 4)])
B46: B45 + floor(Random[(3 * h / 4), (5 * h / 4)])
B47: B46 + floor(Random[(3 * h / 4), (5 * h / 4)])
B48: B47 + floor(Random[(3 * h / 4), (5 * h / 4)])
B49: B48 + floor(Random[(3 * h / 4), (5 * h / 4)])
B50: B49 + floor(Random[(3 * h / 4), (5 * h / 4)])
B51: B50 + floor(Random[(3 * h / 4), (5 * h / 4)])
B52: B51 + floor(Random[(3 * h / 4), (5 * h / 4)])
F_2: (B52, C52)
A55 = NaN
A6 = If(A55 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A55 ≟ 1, Random[0, 1], Random[-1, 0]])
C6 = If(A6 ≟ 0, k, If[A6 ≟ 1, k + Random[3, H], k - Random[3, H]])
F: (B6, C6)
A56 = NaN
A7 = If(A56 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A56 ≟ 1, Random[0, 1], Random[-1, 0]])
C7 = If(A7 ≟ 0, k, If[A7 ≟ 1, k + Random[3, H], k - Random[3, H]])
G: (B7, C7)
A57 = NaN
A8 = If(A57 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A57 ≟ 1, Random[0, 1], Random[-1, 0]])
C8 = If(A8 ≟ 0, k, If[A8 ≟ 1, k + Random[3, H], k - Random[3, H]])
I: (B8, C8)
A58 = NaN
A9 = If(A58 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A58 ≟ 1, Random[0, 1], Random[-1, 0]])
C9 = If(A9 ≟ 0, k, If[A9 ≟ 1, k + Random[3, H], k - Random[3, H]])
J: (B9, C9)
A59 = NaN
A10 = If(A59 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A59 ≟ 1, Random[0, 1], Random[-1, 0]])
C10 = If(A10 ≟ 0, k, If[A10 ≟ 1, k + Random[3, H], k - Random[3, H]])
K: (B10, C10)
A60 = NaN
A11 = If(A60 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A60 ≟ 1, Random[0, 1], Random[-1, 0]])
C11 = If(A11 ≟ 0, k, If[A11 ≟ 1, k + Random[3, H], k - Random[3, H]])
M: (B11, C11)
A61 = NaN
A12 = If(A61 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A61 ≟ 1, Random[0, 1], Random[-1, 0]])
C12 = If(A12 ≟ 0, k, If[A12 ≟ 1, k + Random[3, H], k - Random[3, H]])
N: (B12, C12)
A62 = NaN
A13 = If(A62 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A62 ≟ 1, Random[0, 1], Random[-1, 0]])
C13 = If(A13 ≟ 0, k, If[A13 ≟ 1, k + Random[3, H], k - Random[3, H]])
O: (B13, C13)
A63 = NaN
A14 = If(A63 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A63 ≟ 1, Random[0, 1], Random[-1, 0]])
C14 = If(A14 ≟ 0, k, If[A14 ≟ 1, k + Random[3, H], k - Random[3, H]])
P: (B14, C14)
A64 = NaN
A15 = If(A64 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A64 ≟ 1, Random[0, 1], Random[-1, 0]])
C15 = If(A15 ≟ 0, k, If[A15 ≟ 1, k + Random[3, H], k - Random[3, H]])
Q: (B15, C15)
A65 = NaN
A16 = If(A65 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A65 ≟ 1, Random[0, 1], Random[-1, 0]])
C16 = If(A16 ≟ 0, k, If[A16 ≟ 1, k + Random[3, H], k - Random[3, H]])
R: (B16, C16)
A66 = NaN
A17 = If(A66 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A66 ≟ 1, Random[0, 1], Random[-1, 0]])
C17 = If(A17 ≟ 0, k, If[A17 ≟ 1, k + Random[3, H], k - Random[3, H]])
S: (B17, C17)
A67 = NaN
A18 = If(A67 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A67 ≟ 1, Random[0, 1], Random[-1, 0]])
C18 = If(A18 ≟ 0, k, If[A18 ≟ 1, k + Random[3, H], k - Random[3, H]])
T: (B18, C18)
A68 = NaN
A19 = If(A68 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A68 ≟ 1, Random[0, 1], Random[-1, 0]])
C19 = If(A19 ≟ 0, k, If[A19 ≟ 1, k + Random[3, H], k - Random[3, H]])
U: (B19, C19)
A69 = NaN
A20 = If(A69 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A69 ≟ 1, Random[0, 1], Random[-1, 0]])
C20 = If(A20 ≟ 0, k, If[A20 ≟ 1, k + Random[3, H], k - Random[3, H]])
V: (B20, C20)
A70 = NaN
A21 = If(A70 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A70 ≟ 1, Random[0, 1], Random[-1, 0]])
C21 = If(A21 ≟ 0, k, If[A21 ≟ 1, k + Random[3, H], k - Random[3, H]])
W: (B21, C21)
A71 = NaN
A22 = If(A71 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A71 ≟ 1, Random[0, 1], Random[-1, 0]])
C22 = If(A22 ≟ 0, k, If[A22 ≟ 1, k + Random[3, H], k - Random[3, H]])
Z: (B22, C22)
A72 = NaN
A23 = If(A72 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A72 ≟ 1, Random[0, 1], Random[-1, 0]])
C23 = If(A23 ≟ 0, k, If[A23 ≟ 1, k + Random[3, H], k - Random[3, H]])
A_1: (B23, C23)
A73 = NaN
A24 = If(A73 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A73 ≟ 1, Random[0, 1], Random[-1, 0]])
C24 = If(A24 ≟ 0, k, If[A24 ≟ 1, k + Random[3, H], k - Random[3, H]])
B_1: (B24, C24)
A74 = NaN
A25 = If(A74 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A74 ≟ 1, Random[0, 1], Random[-1, 0]])
C25 = If(A25 ≟ 0, k, If[A25 ≟ 1, k + Random[3, H], k - Random[3, H]])
C_1: (B25, C25)
A75 = NaN
A26 = If(A75 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A75 ≟ 1, Random[0, 1], Random[-1, 0]])
C26 = If(A26 ≟ 0, k, If[A26 ≟ 1, k + Random[3, H], k - Random[3, H]])
D_1: (B26, C26)
A76 = NaN
A27 = If(A76 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A76 ≟ 1, Random[0, 1], Random[-1, 0]])
C27 = If(A27 ≟ 0, k, If[A27 ≟ 1, k + Random[3, H], k - Random[3, H]])
E_1: (B27, C27)
A77 = NaN
A28 = If(A77 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A77 ≟ 1, Random[0, 1], Random[-1, 0]])
C28 = If(A28 ≟ 0, k, If[A28 ≟ 1, k + Random[3, H], k - Random[3, H]])
F_1: (B28, C28)
A78 = NaN
A29 = If(A78 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A78 ≟ 1, Random[0, 1], Random[-1, 0]])
C29 = If(A29 ≟ 0, k, If[A29 ≟ 1, k + Random[3, H], k - Random[3, H]])
G_1: (B29, C29)
A79 = NaN
A30 = If(A79 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A79 ≟ 1, Random[0, 1], Random[-1, 0]])
C30 = If(A30 ≟ 0, k, If[A30 ≟ 1, k + Random[3, H], k - Random[3, H]])
H_1: (B30, C30)
A80 = NaN
A31 = If(A80 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A80 ≟ 1, Random[0, 1], Random[-1, 0]])
C31 = If(A31 ≟ 0, k, If[A31 ≟ 1, k + Random[3, H], k - Random[3, H]])
I_1: (B31, C31)
A81 = NaN
A32 = If(A81 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A81 ≟ 1, Random[0, 1], Random[-1, 0]])
C32 = If(A32 ≟ 0, k, If[A32 ≟ 1, k + Random[3, H], k - Random[3, H]])
J_1: (B32, C32)
A82 = NaN
A33 = If(A82 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A82 ≟ 1, Random[0, 1], Random[-1, 0]])
C33 = If(A33 ≟ 0, k, If[A33 ≟ 1, k + Random[3, H], k - Random[3, H]])
K_1: (B33, C33)
A83 = NaN
A34 = If(A83 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A83 ≟ 1, Random[0, 1], Random[-1, 0]])
C34 = If(A34 ≟ 0, k, If[A34 ≟ 1, k + Random[3, H], k - Random[3, H]])
L_1: (B34, C34)
A84 = NaN
A35 = If(A84 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A84 ≟ 1, Random[0, 1], Random[-1, 0]])
C35 = If(A35 ≟ 0, k, If[A35 ≟ 1, k + Random[3, H], k - Random[3, H]])
M_1: (B35, C35)
A85 = NaN
A36 = If(A85 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A85 ≟ 1, Random[0, 1], Random[-1, 0]])
C36 = If(A36 ≟ 0, k, If[A36 ≟ 1, k + Random[3, H], k - Random[3, H]])
N_1: (B36, C36)
A86 = NaN
A37 = If(A86 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A86 ≟ 1, Random[0, 1], Random[-1, 0]])
C37 = If(A37 ≟ 0, k, If[A37 ≟ 1, k + Random[3, H], k - Random[3, H]])
O_1: (B37, C37)
A87 = NaN
A38 = If(A87 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A87 ≟ 1, Random[0, 1], Random[-1, 0]])
C38 = If(A38 ≟ 0, k, If[A38 ≟ 1, k + Random[3, H], k - Random[3, H]])
P_1: (B38, C38)
A88 = NaN
A39 = If(A88 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A88 ≟ 1, Random[0, 1], Random[-1, 0]])
C39 = If(A39 ≟ 0, k, If[A39 ≟ 1, k + Random[3, H], k - Random[3, H]])
Q_1: (B39, C39)
A89 = NaN
A40 = If(A89 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A89 ≟ 1, Random[0, 1], Random[-1, 0]])
C40 = If(A40 ≟ 0, k, If[A40 ≟ 1, k + Random[3, H], k - Random[3, H]])
R_1: (B40, C40)
A90 = NaN
A41 = If(A90 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A90 ≟ 1, Random[0, 1], Random[-1, 0]])
C41 = If(A41 ≟ 0, k, If[A41 ≟ 1, k + Random[3, H], k - Random[3, H]])
S_1: (B41, C41)
A91 = NaN
A42 = If(A91 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A91 ≟ 1, Random[0, 1], Random[-1, 0]])
C42 = If(A42 ≟ 0, k, If[A42 ≟ 1, k + Random[3, H], k - Random[3, H]])
T_1: (B42, C42)
A92 = NaN
A43 = If(A92 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A92 ≟ 1, Random[0, 1], Random[-1, 0]])
C43 = If(A43 ≟ 0, k, If[A43 ≟ 1, k + Random[3, H], k - Random[3, H]])
U_1: (B43, C43)
A93 = NaN
A44 = If(A93 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A93 ≟ 1, Random[0, 1], Random[-1, 0]])
C44 = If(A44 ≟ 0, k, If[A44 ≟ 1, k + Random[3, H], k - Random[3, H]])
V_1: (B44, C44)
A94 = NaN
A45 = If(A94 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A94 ≟ 1, Random[0, 1], Random[-1, 0]])
C45 = If(A45 ≟ 0, k, If[A45 ≟ 1, k + Random[3, H], k - Random[3, H]])
W_1: (B45, C45)
A95 = NaN
A46 = If(A95 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A95 ≟ 1, Random[0, 1], Random[-1, 0]])
C46 = If(A46 ≟ 0, k, If[A46 ≟ 1, k + Random[3, H], k - Random[3, H]])
Z_1: (B46, C46)
A96 = NaN
A47 = If(A96 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A96 ≟ 1, Random[0, 1], Random[-1, 0]])
C47 = If(A47 ≟ 0, k, If[A47 ≟ 1, k + Random[3, H], k - Random[3, H]])
A_2: (B47, C47)
A97 = NaN
A48 = If(A97 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A97 ≟ 1, Random[0, 1], Random[-1, 0]])
C48 = If(A48 ≟ 0, k, If[A48 ≟ 1, k + Random[3, H], k - Random[3, H]])
B_2: (B48, C48)
A98 = NaN
A49 = If(A98 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A98 ≟ 1, Random[0, 1], Random[-1, 0]])
C49 = If(A49 ≟ 0, k, If[A49 ≟ 1, k + Random[3, H], k - Random[3, H]])
C_2: (B49, C49)
A99 = NaN
A50 = If(A99 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A99 ≟ 1, Random[0, 1], Random[-1, 0]])
C50 = If(A50 ≟ 0, k, If[A50 ≟ 1, k + Random[3, H], k - Random[3, H]])
D_2: (B50, C50)
A100 = NaN
A51 = If(A100 ≟ 0, If[Random[-2, 2] > 0, 1, If[Random[-2, 2]  <  0, -1, 0]], If[A100 ≟ 1, Random[0, 1], Random[-1, 0]])
C51 = If(A51 ≟ 0, k, If[A51 ≟ 1, k + Random[3, H], k - Random[3, H]])
E_2: (B51, C51)
L52: {A, B, C, E, F, G, I, J, K, M, N, O, P, Q, R, S, T, U, V, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2}
L = Sequence(Element[L52, i], i, 1, n + 1)
g = Polynomial(L)
b2: x(Element[L, n + 1])
f(x) = If[a ≤ x ≤ b2, g(x)]
ymin = -4
ymax = 6
departHasard = Random((-n), n)
xrand = 17
yrand = 4
bornesup = Max(Sequence[y(Max[f, x(Element[L, i]), x(Element[L, i + 1])]), i, 1, n])
borneinf = Min(Sequence[y(Min[f, x(Element[L, i]), x(Element[L, i + 1])]), i, 1, n])
D(x) = k
signe = If(Random[1, 4] + n - n ≟ 1, leq, If[Random[1, 4] ≟ 2, lt, If[Random[1, 4] ≟ 3, geq, gt]])
text1: "\text{Déterminer graphiquement les solutions de }f(x)" + (LaTeX[signe]) + "" + (LaTeX[k]) + ""
SolDec = RemoveUndefined(Sequence[Intersect[f, D, x(Element[L, i]) + 0.5, x(Element[L, i + 1]) - 0.5], i, 1, n])
SolInt = RemoveUndefined(Sequence[If[y(Element[L, i]) ≟ k, Element[L, i]], i, 1, n + 1])
Sol = Sort(Sequence[If[i ≤ Length[SolDec], Element[SolDec, i], Element[SolInt, i - Length[SolDec]]], i, 1, Length[SolDec] + Length[SolInt]])
traceSol = Sequence(Segment[Element[Sol, i], (x(Element[Sol, i]), 0)], i, 1, Length[Sol])
correction = 0
dec(x, p) = floor(((x - floor(x)) * 10^(p)))
intervalleDebut = If(signe ≟ geq ∧ (f((a + x(Element[Sol, 1])) / 2) ≥ k), {a, x(Element[Sol, 1]), 1, 1}, If[signe ≟ gt ∧ (f((a + x(Element[Sol, 1])) / 2) > k), If[f(a) > k, {a, x(Element[Sol, 1]), 1, 0}, {a, x(Element[Sol, 1]), 0, 0}], If[signe ≟ leq ∧ (f((a + x(Element[Sol, 1])) / 2) ≤ k), {a, x(Element[Sol, 1]), 1, 1}, If[signe ≟ lt ∧ (f((a + x(Element[Sol, 1])) / 2)  <  k), If[f(a)  <  k, {a, x(Element[Sol, 1]), 1, 0}, {a, x(Element[Sol, 1]), 0, 0}], {-10, -10, 0, 0}]]])
intervalleFin = If(signe ≟ geq ∧ (f((b2 + x(Element[Sol, Length[Sol]])) / 2) ≥ k), {x(Element[Sol, Length[Sol]]), b2, 1, 1}, If[signe ≟ gt ∧ (f((b2 + x(Element[Sol, Length[Sol]])) / 2) > k), If[f(b2) > k, {x(Element[Sol, Length[Sol]]), b2, 0, 1}, {x(Element[Sol, Length[Sol]]), b2, 0, 0}], If[signe ≟ leq ∧ (f((b2 + x(Element[Sol, Length[Sol]])) / 2) ≤ k), {x(Element[Sol, Length[Sol]]), b2, 1, 1}, If[signe ≟ lt ∧ (f((b2 + x(Element[Sol, Length[Sol]])) / 2)  <  k), If[f(b2)  <  k, {x(Element[Sol, Length[Sol]]), b2, 0, 1}, {x(Element[Sol, Length[Sol]]), b2, 0, 0}], {-10, -10, 0, 0}]]])
SolCourbeDebut(x) = If[Element[intervalleDebut, 1] ≤ x ≤ Element[intervalleDebut, 2], g(x)]
SolCourbeFin(x) = If[Element[intervalleFin, 1] ≤ x ≤ Element[intervalleFin, 2], g]
intervalles = RemoveUndefined(Sequence[If[signe ≟ geq ∧ (f((x(Element[Sol, i]) + x(Element[Sol, i + 1])) / 2) ≥ k), {x(Element[Sol, i]), x(Element[Sol, i + 1]), 1, 1}, If[signe ≟ gt ∧ (f((x(Element[Sol, i]) + x(Element[Sol, i + 1])) / 2) > k), {x(Element[Sol, i]), x(Element[Sol, i + 1]), 0, 0}, If[signe ≟ leq ∧ (f((x(Element[Sol, i]) + x(Element[Sol, i + 1])) / 2) ≤ k), {x(Element[Sol, i]), x(Element[Sol, i + 1]), 1, 1}, If[signe ≟ lt ∧ (f((x(Element[Sol, i]) + x(Element[Sol, i + 1])) / 2)  <  k), {x(Element[Sol, i]), x(Element[Sol, i + 1]), 0, 0}]]]], i, 1, Length[Sol] - 1])
SolCourbes = Sequence(If[Element[Element[intervalles, i], 1] ≤ x ≤ Element[Element[intervalles, i], 2], g], i, 1, Length[intervalles])
SolTextDebut = If(Element[intervalleDebut, 1] ≟ -10 ∧ Element[intervalleDebut, 2] ≟ -10 ∨ (Length[intervalles] > 0) ∧ Element[Element[intervalles, 1], 1] ≟ Element[intervalleDebut, 1], "", If[Element[intervalleDebut, 1] ≟ Element[intervalleDebut, 2] ∧ Element[intervalleDebut, 3] ≟ 1 ∧ Element[intervalleDebut, 4] ≟ 1, "\{" + (Element[intervalleDebut, 1]) + "\}", If[Element[intervalleDebut, 3] ≟ 1, "[", "]"] + (If[Element[intervalleDebut, 1] ≟ floor(Element[intervalleDebut, 1]), Element[intervalleDebut, 1] + "", "\simeq " + (floor(Element[intervalleDebut, 1])) + (("," * dec(Element[intervalleDebut, 1], 1)))]) + "; " + (If[Element[intervalleDebut, 2] ≟ floor(Element[intervalleDebut, 2]), Element[intervalleDebut, 2] + "", "\simeq " + (floor(Element[intervalleDebut, 2])) + (("," * dec(Element[intervalleDebut, 2], 1)))]) + (If[Element[intervalleDebut, 4] ≟ 1, "]", "["])] + (If[(Length[intervalles] > 0) ∨ (Element[intervalleFin, 1] ≠ -10) ∨ (Element[intervalleFin, 2] ≠ -10), "\cup ", ""]))
SolTextFin = If(Element[intervalleFin, 1] ≟ -10 ∧ Element[intervalleFin, 2] ≟ -10 ∨ (Length[intervalles] > 0) ∧ Element[Element[intervalles, Length[intervalles]], 2] ≟ Element[intervalleFin, 1], "", If[Element[intervalleFin, 1] ≟ Element[intervalleFin, 2] ∧ Element[intervalleFin, 3] ≟ 1 ∧ Element[intervalleFin, 4] ≟ 1, "\{" + (Element[intervalleFin, 1]) + "\}", If[Element[intervalleFin, 3] ≟ 1, "[", "]"] + (If[Element[intervalleFin, 1] ≟ floor(Element[intervalleFin, 1]), Element[intervalleFin, 1] + "", "\simeq " + (floor(Element[intervalleFin, 1])) + (("," * dec(Element[intervalleFin, 1], 1)))]) + "; " + (If[Element[intervalleFin, 2] ≟ floor(Element[intervalleFin, 2]), Element[intervalleFin, 2] + "", "\simeq " + (floor(Element[intervalleFin, 2])) + (("," * dec(Element[intervalleFin, 2], 1)))]) + (If[Element[intervalleFin, 4] ≟ 1, "]", "["])])
SolText: TableText[{Sequence[If[i > 1, "\cup "] + (If[Element[Element[intervalles, i], 1] ≟ Element[Element[intervalles, i], 2] ∧ Element[Element[intervalles, i], 3] ≟ 1 ∧ Element[Element[intervalles, i], 4] ≟ 1, "\{" + (Element[Element[intervalles, i], 1]) + "\}", If[Element[Element[intervalles, i], 3] ≟ 1, "[", "]"] + (If[Element[Element[intervalles, i], 1] ≟ floor(Element[Element[intervalles, i], 1]), Element[Element[intervalles, i], 1] + "", "\simeq " + (floor(Element[Element[intervalles, i], 1])) + (("," * dec(Element[Element[intervalles, i], 1], 1)))]) + "; " + (If[Element[Element[intervalles, i], 2] ≟ floor(Element[Element[intervalles, i], 2]), Element[Element[intervalles, i], 2] + "", "\simeq " + (floor(Element[Element[intervalles, i], 2])) + (("," * dec(Element[Element[intervalles, i], 2], 1)))]) + (If[Element[Element[intervalles, i], 4] ≟ 1, "]", "["])]), i, 1, Length[intervalles]]}] + (If[(Length[intervalles] > 0) ∧ ((Element[intervalleFin, 1] ≠ -10) ∨ (Element[intervalleFin, 2] ≠ -10)) ∧ (Element[Element[intervalles, Length[intervalles]], 1] ≠ Element[intervalleFin, 1]) ∧ (Element[intervalleFin, 1] ≠ Element[intervalleFin, 2]), "\cup ", ""])
SolTextUnion = If(Length[SolTextDebut] ≟ 0 ∧ Length[SolTextFin] ≟ 0 ∧ Length[SolText] ≟ 0, "\emptyset", SolTextDebut + SolText + SolTextFin)
text2: "\text{Solution de } f(x)" + (LaTeX[signe]) + " " + (LaTeX[k]) + " :\\\\ \mathcal{S} =" + (LaTeX[SolTextUnion]) + ""